A Space-Diffused Spatial-Temporal ARray ... - Athanassios Manikas

A Space-Diffused Spatial-Temporal ARray (STAR) Receiver for DS-CDMA System

A Space-Diffused Spatial-Temporal ARray (STAR) Receiver for DS-CDMA System Jason Wee Peng Ng and Athanassios Manikas Communications and Signal Processing Research Department of Electrical and Electronic Engineering Imperial College London http://skynet.ee.ic.ac.uk/manikas.html and http://skynet.ee.ic.ac.uk/ng.html International Journal in Hellenic European Research in Mathematics & Informatics Science, 2004

ABSTRACT In this paper, a blind space-time receiver is proposed to handle point and diffused sources for asynchronous multipath DS-CDMA systems. The receiver is based on a computationally efficient subspace-type algorithm for its joint space-time channel estimation which is insusceptible to near-far problems. The coherency between the sources is removed by a novel temporal smoothing technique operating in the transformed domain. Unlike many conventional DS-CDMA receivers, the proposed formulation and approach is applicable even with the presence of co-code interferers. Furthermore it is robust to channel estimation errors in the event of any unidentified (incomplete) or erroneous (incorrect) channel parameter.

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NOMENCLATURE E E a·bX ÐÞÑ‡ a·bL i·j Œ diagaEb expaEb traceÐ Ñ detÐ Ñ E, 0R ˆR

Scalar Column Vector Matrix Transpose Complex conjugate Hermitian transpose Round up to integer Kronecker product Diagonalisation of vector E Element by element exponential of vector E Trace of matrix Determinant of matrix Element by element power Zero vector of R elements Identity matrix of R ‚ R dimension

I. INTRODUCTION Traditional sensor array processing frequently assumes a simplistic pictorial of the multipath environment which is modeled as an assemblage of point sources. However in a typical wireless communication system, particularly in an urban or suburban setup, the signal transmitted into the channel suffers multiple reflections, diffraction and scattering which will inevitably result in a diffusion of its signal component. This hence leads to a performance degradation when conventional processing techniques, based on point sources scenario, are applied c1d. Thus it is paramount to adopt a generalised diffusion framework in order to achieve an effective system design.

In the recent years, several experimental measurements c2-5d have been conducted in

practical setups to demonstrate the significance and effect of signal diffusion. For instance, the deteriorating impact of diffused signals on system performance via beamforming is

reported in c2d. These results further emphasise and establish the importance of incorporating the diffusion framework in order to cope with multiple diffused/point sources environments. But, despite its importance, not many works have been published in the treatment of diffused sources, especially in the receiver design to handle both diffused and point sources. Several

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parametric approaches in the estimation of the diffused sources have however being introduced. For instance, Meng et al suggested the DISPARE (Dispersed Signal Parametric

Estimation) c6d method which is based on the weighted projection of the eigenvectors of the signal covariance matrix onto the estimated quasi-noise subspace, with the assumption that the number of sources present at the array are known a priori. Valaee et al, on the other hand,

developed the DPSE (Distributed Signal Parameter Estimator) c7d algorithm which involves mimimizing a certain norm of the transformed noise eigenvectors in the signal subspace, provided that the spatial correlation of the distributed signal belongs to a parametric class. In

c8d, Wu et al introduces the vec-MUSIC algorithm by applying the principle of MUSIC based on mathematical operator properties to interpret the geometric structure of the covariance matrix of the vectorised outer-product of the data. All these three techniques: DISPARE, DSPE and vec-MUSIC algorithms, which are basically modifications from classical MUSIC algorithm, provide the parametric localisation, that is the nominal direction of arrival, of the diffused sources. Following that, the angular spread estimation, in conjunction with its

nominal direction of arrival, are subsequently been investigated in c9-12d. A computationallylow complexity estimator is proposed in c11d to provide estimates of both the direction of

arrival and angular spread of the diffused signal; whereas in c12d, the estimates are decoupled and optimise using two successive single-dimensional minimisations. With these two

estimates, beamforming techniques, such as the broad-null beamformer devised in c13d, can then be applied in its reception process. In this work, however, an asynchronous blind space-time receiver is proposed, without having to perform angular spread estimation, for both point and/or diffused multipath DSCDMA systems. Its channel estimation technique is derived from the efficient near-far

resistant PADE (polarisation-angle-delay estimation) algorithm c14-16d employed in diversely polarised arrays to provide its joint angle and delay estimation. Such adaption of algorithm from diversely polarised arrays has been utilised in c17, 18d to obtain the direction of arrival

estimates, but it excludes the temporal dimension in its estimation operation; hence the estimation algorithm in c15d is attempted in c19d, but its estimation procedure is not as

compact and efficient and can only be completed after a few tens of observation intervals Page 3


(bursts). However in this paper, a more computationally efficient near-far resistant channel estimation algorithm is proposed which is then being employed and integrated as the frontend of a novel blind space-time receiver. As a result of its novel underlying architecture, the receiver can also be easily extended to cope in a co-code environment. The resulted receiver is robust against any unidentifiable or erroneous channel parameter resulted in the estimation process. It is optimum with respect to the SIR criterion and is able to achieve (asymptotically) complete

interference

cancellation. Computer simulation studies demonstrate the

effectiveness of the proposed approach and it is shown to perform just as well even when the signal components are co-located in either one/two of the space, time or code domains. The rest of the paper is organised as follows. Section II presents the model used for the diffused and point multipath signals in co-code DS-CDMA systems. The joint space-time channel estimation algorithm is then described in Section III, together with the formulation of the receiver design which is easily extendable in a co-code environment. Following that, Section IV provides several simulation studies which depict the performance of the proposed diffusion-based receiver. The paper is finally concluded in Section V.

II. SIGNAL MODEL Consider an Q -user asynchronous DS-CDMA system, with the modulating information signal associated with the 3th user given as a function of the symbol index 8 and chip index : as 73 a>b

" a3 c8d " !3 c:d- a> _

œ

8œ _

a- " :œ!

8X-=

:X- b

a1b

where {a3 c8d − „ 1ß a8 − m} is the 3th user's data symbol, X-= is the channel symbol period, {!3 c:d − „ 1ß : œ !ß "ß á ß a-

"} corresponds to the 3th user's pseudo-noise spreading

sequence of period a- œ X-= ÎX- , and -Ð>Ñ denotes the chip pulse-shaping waveform of duration X- .

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3 th Mobile Station

)34

th

4 Scattering Cluster

Base Station

534 Figure 1: Scattering propagation channel.

Suppose the transmitted signal due to the 3th user arrives at the base station, employing an

array of R antenna sensors, via O3 scattering clusters c20d as shown in Fig. 1. The complex

baseband signal vector pertaining to the 4th cluster, consisting of P34 scatterers, can therefore be modelled as a superposition of all the scatterers' contribution within the cluster, expressed as ""345 WÐ)34 P34

s34 Ð>Ñ

œ

~ ) 345 Ñ 73 Ð>

7345 Ñ

5œ"

a2b

~ where "345 , ) 345 , 7345 denotes respectively the complex fading coefficient, angular perturbation about the cluster's nominal direction )34 , and time delay of the 5 th scatterer from the 4th cluster corresponding to the 3th user. The manifold vector WÐ)Ñ œ exp(

4 Þ [

734 Ñ

734 Ñ

Ð3Ñ

P34 P34 P34 ~ ‰ ! ! ! ˆ where ,34 œ "345 and :34 œ "345 ) 345 ‚ "345 represent the cluster's aggregate fading 5œ"

5œ"

5œ"

coefficient and the weighted perturbation factor respectively. Notice that in the case of lineof-sight scenario with no angular spreading, the above framework in a3b can still be utilised since :34 œ ! for zero angular perturbation. · By denoting E34 ˜ œ ˜WÐ)34 Ñ :34 WÐ)34 Ñ™, and letting ,3" ß ,32 ß á ß ,3O3 ‘ and 73 Ð>Ñ œ 73 Ð> X

73" Ñß 73 Ð>

3

œ E3" ß E32 ß á ß E3O3 ‘, ,3 œ

732 Ñß á ß 73 Ð>

73O3 Ñ‘ , the net X

baseband vector representation of the received signal in the presence of additive isotropic white Gaussian noise with double sided power spectral density R! Î# can therefore be shown to be given by

Ba>b

œ

Þ diagˆ,‰ Þ 7Ð>Ñ

a 4b

nÐ>Ñ

where nÐ>Ñ is the complex white Gaussian noise vector and œ

"ß

2ß

áß

,

œ

,X" ß

,X2 ß

áß

7Ð>Ñ

œ

7X" Ð>Ñß

7X2 Ð>Ñß

Q‘ X ,XQ ‘

áß

7XQ Ð>Ñ‘

X

Taking the clusters' delay to lie within the range Ò!ß X-= Ñ, the R -dimensional signal vector

Ba>b, received from the sensors output, is then sampled at a rate of "ÎX= and passed through a bank of R tapped-delay lines (TDL), each of length #;a- . Upon concatenating the contents of the TDLs, the #;R a- -dimensional discretised signal vector is thus formed and read for every

X-=

with

the

8th

observation

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interval

represented

as


Bc8d œ B" c8dX ß B2 c8dX ß

âß

X BN c8dX ‘ , where B5 c8d is the #; a- -dimensional discretised

output frame from the 5 th TDL. To model the inclusion of the discretised temporal dimension, the manifold vector E34 due to the 4th cluster of the 3th user is modified to form the spatio-temporal array (STAR) manifold vector ¡34 expressed as ˜ œ

¡34

E34 Œ ‰634 œ 3

Ð5Ñ

where 634 œ °734 ÎX= ± is the discretised cluster's delay; the matrix ‰ (or ‰X ) is a #; a- ‚ #; atime down-shift (or up-shift) operator matrix given as follows !X#; a‰œ– ˆ#; a-

" "

! !#; a-

"

a6b

—

and œ 3 is related to the 3th user's PN-code sequence defined as " ! 3 c : d Þ ‰: ; -

a7b

a- "

œ3

œ

:œ!

with the vector - being the oversampled chip-level pulse shaping function -Ð>Ñ padded with zeros at the end, i.e. -

œ

-Ð!Ñß -ÐX= Ñß

âß

-ÐÐ;

"ÑX= Ñß

!X;Ð#a-

"Ñ

‘

X

a8b

Now by taking user 1 as the desired user of interest, the net spatio-temporal discretised

signal vector Bc8d can thus be written as – Bc8d œ ‡" †" a" c8d

– "‡ 3 †3 a3 c8d Y"

3œ#

– " ‡ 3 †3 a3 c8d Q

3œY" "

nc8d

a9b

where the first term on the right-hand side of a9b denotes the discretised signal vector associated with the desired user, the second term contains the interferences due to aY"

"b of

its co-code users (arising from either code-reuse interferers or intercepting co-code jammers), the third term represents the remaining interferences from the rest of the users together with their corresponding co-code partners, and the last term is the sampled noise vector. The 3th user's data vector constitutes contributions from not only the current but also the previous and

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next symbols given as a3 c8d œ c a3 c8 "dß a3 c8dß a3 c8 "d dX , the matrix †3 œ ˆ$ Œ ,3 , and – ‡3 œ ˆˆR Œ Ð‰X Ñ; a- ‰‡3 ß ‡3 ß ˆˆR Œ ‰; a- ‰‡3 ‘, with ‡3 having columns the STAR manifold vectors corresponding to the 3th user, i.e. ‡3 œ ¡3" ß ¡32 ß á ß ¡3O ‘Þ 3

III. CHANNEL ESTIMATION AND RECEPTION To perform an estimation of the channel parameters pertaining to the desired user and all

of its co-code interferers, we proposed that the discretised signal vector Bc8d in a9b be preprocessed

by

the

desired

user's

preprocessor

(i.e.

user

1)

defined

as

™" œ ˆR Œ ˆdiagÐ~œ " Ñ " …‰, where ~œ " is the Fourier transformed version of œ " , that is ~œ " œ …œ " with … being the Fourier transformation matrix given by Q0 , Q1 , Q2 , á , QÐ2; a-

… œ

1Ñ

‘

where Q œ ", Q1 , Q2 , á , QÐ2; a21 ‰ with Q œ expˆ 4 2; a-

Ð10Ñ

1Ñ ‘X

To get a clearer picture of its operation on the discretised signal vector Bc8d, let's apply the preprocessor to the STAR manifold vector in a5b as follows ¡˜ 34

œ œ œ

™" ¡34

E34 Œ ˜diagÐ~œ " Ñ " …Ð‰634 œ 3 Ñ™ E34 Œ ˜diagÐ~œ " Ñ " diagÐ~œ 3 Ñ Q634 ™

Ð11Ñ

It is clear that the above expression in a11b can be reduced to simply ¡˜ "4 œ E"4 Œ Q6"4 if and only if 3 œ ", which is corresponding to the desired user's PN-code sequence. Hence by applying the same operation to a9b, the discretised signal vector is therefore transformed to D " c 8d

œ

™" Bc8d

˜ 3 ,3 a3 c8d "‡ Y"

œ

3œ"

™" M ISI c8d

™" M MAI c8d

™" nc8d

Ð12Ñ

˜ 3 œ ¡˜ ß ¡˜ ß á ß ¡˜ ‘. Notice that the signal vector D " c8d is effectively decoupled where ‡ 3" 32 3O

˜ " ," a" c8d as well as that of its into four terms, namely the desired signal constituent ‡ 3

aY"

"b co-code partners, the ISI, MAI and noise components respectively.

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But its second order statistics ‘D " − V2;R a- ‚2;R a- , instead of providing a basis for the desired signal subspace, would result in a rank deficiency with the desired signal subspace dimension being reduced to one. To restore the dimensionality of this subspace back to ! O3 , Y"

3œ"

˜ 3 provided by the we will make use of the Vandermonde structure of the submatrices of ‡ preprocessing operation. This can be achieved by performing a technique referred to as temporal smoothing. First let's partition the correlation matrix ‘D " into R # segmented matrices of size 2; a- ‚ 2; a- . By averaging a set of U (where U œ 2; a.

.

" and

2; a- ) overlapping . ‚ . submatrices along the main diagonal of each segmented

matrices simultaneously, a R . ‚ R . temporal-smoothed covariance matrix ‘Tsmooth is therefore constructed. However its dimensionality can only be successfully restored provided that U ! O3 . Note that such averaging operation is similar to the well known spatial Y"

3œ"

smoothing (averaging) technique as described in c21d. This technique can also be applied for clusters arriving from the same direction (co-directional). But for clusters of a particular user arriving at the same time (co-delay), singularity in ‘Tsmooth will occur. This special case cannot be resolved for a general array geometry but for a uniform linear array where spatial smoothing can be overlaid on top of ‘Tsmooth to form the spatial-temporal-smoothed covariance matrix ‘STsmooth . Having obtained the covariance matrix, the clusters' channel parameters can be found by minimising the following MUSIC-type cost function, which is derived using the transformed STAR manifold vector ¡˜ , given as 0Ð)ß 6ß :Ñ

œ

L ˜ ¡˜ „n „L n ¡

a13b

where ¡˜ œ E Œ Q6. in which Q. is a subvector of Q with length . , and „n is a matrix whose columns are the generalised noise eigenvectors of (‘STsmooth , ƒ) due to the transformed noise in a12b, with ƒ representing the spatial-temporal-smoothed diagonal matrix ™" ™L " .

However, the minimisation process involves a multidimensional search over ), 6 and : for its minima. To simplify the process, it is noted that the manifold vector E within the transformed STAR manifold vector ¡˜ can be rewritten as EÐ)ß :Ñ œ ŒÐ)Ñ Þ :Ð:Ñ where

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· WÐ)Ñ ‘

ŒÐ)Ñ œ WÐ)Ñ

:Ð:Ñ œ c "

à

: dX

a14b

Note that for a linear array geometry, for instance an array lying along the B-axis, the term · WÐ)Ñ will be nullified for ) œ ! and 1 due to its derivative coefficient being proportional to · an azimuth-dependent function sinÐ)Ñ. In this case, the true WÐ)Ñ can be replaced by lumping its azimuth-dependent function together with :, i.e. ŒÐ)Ñ œ ÒWÐ)Ñß HÐ)ÑÓ and :Ð:ß )Ñ œ Ò"ß · :sinÐ)ÑÓX where HÐ)Ñ is the derivative term WÐ)Ñ after discarding its azimuth-dependent function.

The re-expression in a14b thus yields a cost function similar to that commonly-used for

diversely polarised arrays c14, 16d given as 0Ð)ß 6ß :Ñ

6 :L ðóóóóóóóóóóóóóñóóóóóóóóóóóóóò ÐŒ Œ Q6d ÑL „n „L n ÐŒ Œ Qd Ñ :

œ

•˜ œ”

@"" @#"

@"# @## •

a15b

As in the diversely polarised arrays scenario, the minimisation over the : search space is equivalent to finding the eigenvectors corresponding to the minimum eigenvalues of •. Hence by dropping the two-dimensional vector : and applying the quadratic formula, the cost function in (15) can be simplified to 0Ð)ß 6Ñ

œ

traceÐ•Ñ

ÈtraceÐ•Ñ#

%detÐ•Ñ

a16b

where traceÐñÑ denotes the trace operation and detÐñÑ represents the determinant of the 2 ‚ 2 matrix. Now let 0min be the minima obtained from the spectrum constructed using the cost function 0Ð)ß 6Ñ in (16). The location of the minima, as such, provides the joint estimate of its direction of arrival (DOA) and time of arrival (TOA). Its corresponding weighted perturbation factor, on the other hand, is estimated as follows : s

œ

Ú Ð0

#@"" ÑÎ#@"# min or Û Ü #@#" ÎÐ0min #@## Ñ

a17b

However in the case of a linear array, the estimated weighted perturbation factor : s has to be divided by its azimuth-dependent term sinÐs ) Ñ. It is also worthwhile to note that the above

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expression in a17b can be further simplified in most circumstances since the value 0min is usually close to zero. Now for a set of F unique PN-code signatures, the estimated composite channel parameters can be obtained as s comp ‡

œ

s T Rß" ß ‡

s T Rß2 ß ‡

âß

s T RßF ‘ ‡

a18b

s T Rß? has columns the estimated STAR manifold vectors associated with all the users where ‡ sharing the ?th PN-code signatures. In order for the blind space-time receiver to suppress the contributions from the MAI and ISI interferences, it is proposed that the received discretised signal vector Bc8d in a9b be passed through a novel multi-cluster filter bank to yield Cc8d

œ

‹L Þ Bc8d

a19b

where ‹ is the multi-cluster filter bank based on the orthogonal projection of the interference subspace, i.e. ‹

œ

¼ s s interf ‡T Rß" ‡

sL Š‡ T Rß"

¼ s s interf ‡T Rß" ‹ ‡

"

a20b

s interf œ ˆˆR Œ Ð‰X Ñ; a- ‰‡ s comp ß ‡ s aT R ß"b ß ˆˆR Œ ‰; a- ‰‡ s comp ‘, in which ‡ s aT R ß"b is the where ‡ comp comp s comp with the exclusion of the matrix ‡ s T Rß" œ estimated composite channel parameters ‡

s "ß ‡ s #ß á ß ‡ s Y" ‘ corresponding to the desired user's PN-code sequence. ‡

In a non co-code environment, the outputs of the filter bank can then be simply combined to realise the decision statistic for the 8th symbol of the desired user ,c8d

œ

A L Þ C c8 d

a21b

where A is the combining weight vector obtained using the principal eigenvector of the

autocorrelation matrix of a19b. But such methodology will result in an arbitrary phase ambiguity which can however be easily resolved by differential encoding, with the transmitted data symbol /3 c8d œ /3 c8

criterion s / 3 c8d œ sgn(V/{,c8

"d.a3 c8d and the decoding according to the following

"d‡ .,c8d}).

On the other hand, in the presence of co-code users, the filter bank output, comprising of

! O3 branches, need to be partitioned to differentiate those branches belonging to the desired Y"

3œ"

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user. This can done by assigning a short random header sequence common to the designated non co-code user group. The filter bank output, following the decision device, are then passed to the Branch Identification Process, whereby a correlation with the header is performed to identify the dominant branch exhibiting the strongest presence of the header sequence. The dominant branch is subsequently cross-correlated with each of the ! O3 branches and Y"

3œ"

compared with a prespecified threshold value. When the correlated output exceeds the threshold value, it is assigned to the desired user. Having segregated the branches, the desired

user's filter bank outputs can then be combined using a21b. Note that it is not necessary to assign all the O" branches to the desired user. If the channel parameters of any particular branch is erroneous (incorrect channel estimation) or unidentified (incomplete channel estimation), the Branch Identification Process will leave that branch unassigned, thus inducing robustness to the receiver. In a similar manner, the above technique can also be applied to decode the remaining users in the designated group as well as their corresponding co-code partners. The complete procedure outlining the major steps of the proposed channel estimation and reception process is summarised as shown below: 1. Sample the array output and concatenate the tapped-delay lines (TDL) contents to form the discretised signal vector in a9b.

2. Next, apply the desired user's preprocessor onto the discretised signal vector as shown in a12b.

3. Following that, form the matrix ‘smooth by performing the temporal smoothing technique to restore the dimensionality of the desired signal subspace. 4. Then carry out the generalised eigenvector decomposition of ‘smooth and apply the cost function in (16) to obtain the joint space-time channel estimation. Its corresponding weighted perturbation factor are estimated using a17b.

5. Based on the estimated channel parameters, compute the multi-cluster filter bank and apply it onto the discretised signal vector as described in a19b and (20).

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6. If the environment is non co-code, simply combine the outputs of the filter bank, as shown in a21b, by using the principal eigenvector of the autocorrelation matrix of a19b.

7. If the environment is co-code, apply the Branch Identification Process to segregate the output branches belonging to the desired user's and combined them using step 6.

IV. SIMULATION STUDIES To demonstrate the key features of the proposed blind space-time receiver, let's consider a uniform R œ 5 element circular array (with half-wavelength spacing) operating in the presence of Q œ 7 co-channel DS-CDMA users, each being assigned a Gold sequence of length a- œ 31 (of rectangular chip pulse-shaping). The number of unique code signatures is F œ 3, with the designated user group consisting of 3 œ ", 3 and 6, as listed in Table I. The angular spread 5 (SPD) of each cluster is rendered by generating 40 spatially uniformdistributed local scatterers. The array is assumed to collect 150 data symbols for processing with a chip-rate sampler of ; œ 1.

TABLE I: USERS' PARAMETERS Code signature vector " (!" ) Code signature vector # (!# ) Code signature vector $ (!$ ) (user 3, cluster 4) DOA TOA SPD (user 3, cluster 4) DOA TOA SPD (user 3, cluster 4) DOA TOA SPD (3, 4) œ (", ") "#!‰ &X- !‰ (3, 4) œ ($, ") #$!‰ %X- "Þ*‰ (3, 4) œ (', ") "'!‰ "%X- #Þ'‰ (3, 4) œ (", #) "(!‰ #&X- "Þ$‰ (3, 4) œ ($, #) #&!‰ "!X- $Þ%‰ (3, 4) œ (', #) "*!‰ $!X- %Þ&‰ (3, 4) œ (", $) #&!‰ "!X- !Þ&‰ (3, 4) œ ($, $) $&!‰ ##X- &Þ!‰ (3, 4) œ (', $) #!!‰ #)X- "Þ(‰ (3, 4) œ (", %) $!!‰ #!X- %Þ#‰ (3, 4) œ (%, ") &!‰ %X- %Þ#‰ (3, 4) œ (', %) #!!‰ #"X- !‰ (3, 4) œ (#, ") '!‰ "!X- #Þ%‰ (3, 4) œ (&, ") )!‰ ")X- !‰ (3, 4) œ (', &) $#!‰ "'X- $Þ)‰ (3, 4) œ (#, #) "(!‰ "&X- !‰ (3, 4) œ (&, #) "#!‰ "&X- !Þ"‰ (3, 4) œ ((, ") "!‰ $X- !Þ*‰

Let's assume that user 1 is the desired user having an input SNR of 20dB; while its corresponding co-code partner (i.e. user 2) constitutes an interference ratio of 0dB, together with the rest of the remaining interferers having a SIR œ -20dB (i.e. near-far problem). By setting . œ 55 for temporal smoothing, it is seen from Fig. 2 that all the clusters, be it diffused or line-of-sight occurrences, associated with the desired user as well as its co-code partners can be identified/estimated successfully using the proposed algorithm. Notice that

Page 13


the algorithm can still operate even in situations whereby (i) the 2nd cluster of user 1 is colocated in both the code and space domains due to the 2nd cluster of user 2, (ii) the 3rd cluster of user 1 is co-located in both the code and time domains due to the 1st cluster of user 2, and (iii) the 3rd cluster of user 1 is co-located in both the space and time domains due to the 2nd cluster of user 3. In addition to that, the number of clusters that can be resolved by the algorithm is also not constrained by the number of sensors available in the array.

30

170.26, 25.000 25

299.59, 20.000

TOA (Tc)

20

169.93, 15.000 15

60.37, 9.999

249.85, 10.000

10

120.14, 5.000 5

0 0

60

120

180

240

300

360

DOA (deg)

(a)

(b)

Figure 2: MUSIC-type spectrum of the desired user (i.e. user 1 with code signature vector !" ) and its co-code partners.

The clusters belonging to the desired user are then singled out from its corresponding cocode partner, as illustrated in Table II, by applying the Branch Identification Process with an header sequence of length 7. Fig. 6 depicts the signal constellation of (a) the proposed · diffusion-based receiver (i.e. adhering EÐ)ß :Ñ œ WÐ)Ñ :WÐ)Ñ framework) as compared with (b) its equivalent non-diffusion counterpart (i.e. adhering EÐ)Ñ œ WÐ)Ñ framework), as well as with (c) a diffusion-based ST (Space-Time) decorrelating detector, and (d) a diffusion-based 2D (2-Dimensional) RAKE receiver, with the latter three assuming full knowledge of the channel information (including knowledge of all the desired user's co-code interferences). It is clear that by incorporating the diffusion framework, the proposed

Page 14


diffusion-based receiver offers a considerable performance enhancement than that of its nondiffusion counterpart. Furthermore, even with all the receivers adopting the diffusion framework, the proposed receiver performs significantly much better than that of the 2D RAKE receiver, with its performance approaches that of a ST decorrelating detector.

TABLE II: (3 user, 4th cluster) Correlated output th

BRANCH IDENTIFICATION PROCESS (User 1) (", ") (", #) (", $) (", %) (#, ") (#, #) "Þ!!!! !Þ**** "Þ!!!! "Þ!!!! !Þ!"&" !Þ!"&"

0.03

0.4 0.3

0.02

Imaginary part

Imaginary part

0.2 0.01

0

-0.01

0.1 0 -0.1 -0.2

-0.02

-0.3

-0.03 -1

2

x 10

-0.5

0

0.5

1

-0.4 -2

-1.5

-1

-0.5

0

Real part

Real part

(a)

(b)

0.5

1

1.5

2

5

10

15

20

-3

15

1.5 10

Imaginary part

Imaginary part

1 0.5 0 -0.5

5

0

-5

-1 -10

-1.5 -2 -1.5

-1

-0.5

0

0.5

1

1.5

-15 -20

-15

-10

-5

0

Real part

Real part

(c)

(d)

Figure 3: Constellation diagram of user 1 with (a) the proposed diffusion-based receiver, (b) its equivalent non-diffusion counterpart, and diffusion-based (c) ST decorrelating detector and (d) 2D RAKE receiver.

Page 15


In a similar manner, the constellation diagram of its co-code partner, that is user 2, can also be obtained as illustrated in Fig. 4a. Thus far, we have seen the near-far resistant capability of the proposed algorithm in the presence of strong non co-code interferers, with each contributing a SIR œ -20dB. Now, lets consider the effect of having a near-far situation contributed by its corresponding co-code partner. Using the same scenario as above, the power of user 1 is increased 30dB above that of its co-code partner, user 2. By applying the same algorithm, the resulting constellation diagram of user 2 is plotted as depicted in Fig. 4b. Comparing with the strong non co-code interferers case as seen in Fig 4a, little deteriorating effect is being observed from its resulting signal constellation. It is therefore conclusive that the algorithm is near-far resistant regardless of whether the interferers come from co-code or unique-code groups.

0.03

0.04 0.03

0.02

Imaginary part

Imaginary part

0.02 0.01

0

-0.01

0.01 0 -0.01 -0.02

-0.02 -0.03 -0.03 -1.5

-1

-0.5

0

0.5

1

1.5

-0.04 -1.5

-1

-0.5

0

Real part

Real part

(a)

(b)

0.5

1

1.5

Figure 4: Constellation diagram of co-code partner (user 2) with user 1 constituting (a) an interference ratio of 0dB and (b) an interference ratio of 30dB.

To illustrate the robustness of the receiver against channel estimation errors, let's take user 3 as the desired user in the designated group, with its 1st cluster yielding erroneous channel parameters and its 3rd cluster unidentified in the channel estimation process. Its corresponding space-time spectrum is plotted as shown in Fig. 5. Note that its 1st cluster Ð#$!‰ ß %X- Ñ yields an

Page 16


erroneous channel parameters of Ð179.87‰ ß 6.999X- Ñ and its 3rd cluster Ð$&!‰ ß ##X- Ñ is unidentified as can be seen from the 2D spectrum of Fig. 5b.

30

25

350, 22

TOA (Tc)

20

80.09, 18.000

15

119.84, 15.000

250.21, 10.000

10

5

0

50.32, 4.000

60

179.87, 6.999

120

180

240

300

360

DOA (deg)

(a)

(b)

Figure 5: Space-time spectrum of user 3 together with its corresponding co-code partners (all sharing the code signature vector !2 ).

Similarly, by applying the Branch Identification Process (as shown in Table III) and setting the prespecified threshold value to, say 0.5, the constellation diagram of user 3 employing (a) the proposed receiver is compared with (b) its corresponding diffusion-based ST decorrelating detector as depicted in Fig. 6. As a result of the robustness induced by the Branch Identification Process in the receiver architecture, the signal constellation due to the proposed receiver is much better and more well-defined than that of the ST decorrelating detector. Notice also that the only identifiable and estimable cluster produced by the Branch Identification Process, that is the 2nd cluster of user 3, is co-located both in space and time with the 3rd cluster of user 1. Hence, it is evident that so long as there exists a single identifiable and estimable cluster due to the desired user separable in at least one of the space, time or code domains, the proposed receiver will be robust to any other erroneous (incorrect channel estimation) or unidentified (incomplete channel estimation) channel parameters incurring at the front-end estimation phase.

Page 17


TABLE III: BRANCH IDENTIFICATION PROCESS (User 3) (3 user, 4th cluster) ($, ") ($, #) ($, $) (%, ") (&, ") Correlated output !Þ"*' "Þ!!!! n.a. !Þ!(&% !Þ!$&# th

0.03

(&, #) !Þ!$&#

0.05 0.04 0.03 0.02

0.01

Imaginary part

Imaginary part

0.02

0

-0.01

0.01 0 -0.01 -0.02 -0.03

-0.02

-0.04 -0.03 -1.5

-1

-0.5

0

0.5

1

1.5

-0.05 -0.15

-0.10

-0.05

0

Real part

Real part

(a)

(b)

0.05

0.10

0.15

Figure 6: Constellation diagram of user 3 with diffusion-based (a) proposed receiver and (b) ST decorrelating detector, in the presence of incomplete or incorrect channel estimation.

Next, let's take a closer look at the performance of the receiver with framework based on · (i) the proposed diffusion model EÐ)ß :Ñ œ WÐ)Ñ :WÐ)Ñ as compared with that based on (ii) the conventional non-diffusion model EÐ)Ñ œ WÐ)Ñ. For comparison clarity, lets assume that the all the clusters under consideration have the same angular spread 5. Using the same setting as in Table I, the output SNIR of the receivers are averaged over 1000 Monte Carlo runs and plotted as shown in Fig. 7. It is therefore apparent that by incorporating the diffusion aspect into the framework, the proposed receiver provides a substantial performance gain than that based on the conventional model which is observed to be deteriorating with the angular spread 5.

Page 18


45

Average output SNIR (dB)

40 35 30 25 20 15 10 Rx based on proposed model, EÐ)ß:Ñ Rx based on conventional model, EÐ)Ñ

5 0

0

1

2

3

4

5

6

7

8

9

10

Angular spread (deg)

Figure 7: SNIR performance of receiver based on (i) proposed model EÐ)ß :Ñ œ WÐ)Ñ and (ii) conventional model EÐ)Ñ œ WÐ)Ñ, versus the angular spread 5.

· :WÐ)Ñ

Having seen the benefit of including the diffusion model in the receiver framework, let's assess the performance of the proposed receiver architecture in terms of output SNIR versus input SNR, together with the conventional ST decorrelating detector and 2D RAKE receiver. For fairness in comparison, the diffusion framework will be integrated into all the receivers under consideration. As expected, the output SNIR of the proposed receiver is much higher than that of the RAKE receiver; and its performance closely follows that of the ST decorrelating detector.

Page 19


45 40

Average output SNIR (dB)

35 30 25 20 15 ST decorrelating detector Proposed receiver 2D RAKE receiver

10 5 0 -5

0

2

4

6

8

10

12

14

16

18

20

Input SNR (dB)

Figure 8: Output SNIR versus input SNR of (i) proposed receiver, (ii) ST decorrelating detector, and (iii) 2D RAKE receiver

V. CONCLUSIONS A blind space-time receiver based on a computationally efficient near-far resistant channel estimation technique is presented for multiple point or diffused signal paths in an asynchronous DS-CDMA system. Due to its underlying architecture, the receiver can be easily extended to cope in a non-unique code signature environment by simply adding a novel Branch Identification Process in the detection procedure. The receiver is robust to erroneous or incomplete channel estimation since its operation requires only the existence of an estimable cluster due to the desired user separable/identifiable in at least one of the following domains: space, time and code. The number of resolvable clusters is also no longer limited by the number of sensors available in the array.

Page 20


ACKNOWLEDGEMENT The work reported in this paper is supported by the Engineering and Physical Sciences Research Council (EPSRC) UK, under the research grant GR/R08148/01.

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[2]

K. I. Pedersen, P. E. Mogensen and B. H. Fleury, "Spatial channel characteristics in outdoor environments and their impact on BS antenna system performance", IEEE Proc. VTC, vol. 2, pp. 719723, May 1998.

[3]

M. Larsson, "Spatio-temporal channel measurements at 1800 MHz for adaptive antennas", IEEE Proc. VTC, vol. 1, pp. 376-380, May 1999.

[4]

A. Kuchar, J. P Rossi and E. Bonek, "Directional macro-cell channel characterization from urban measurements", IEEE Trans. Antennas Propagation, vol. 48, no. 2, pp. 137-146, Feb 2000.

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Y. Meng, P. Stoica and K. M. Wong, "Estimation of the directions of arrival of spatially dispersed signals in array processing", IEE Proc. Radar, Sonar and Navig., vol. 143, no. 1, pp. 1-9, Feb 1996.

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[8]

Q. Wu, K. M. Wong, Y. Meng and W. Read, "DOA estimation of point and scattered sources - VecMusic", IEEE SP Workshop on Stat. Sig. and Array Proc., pp. 365-368, Jun 1994.

[9]

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[10]

Q. Wan, J. Yuan, Y. N. Peng, W. L. Yang and K. P. Long, "Estimation of nominal direction of arrival and angular spread using the determinant of the data matrix", Int. Workshop on Mobile and Wireless Comms. Network, pp. 76-79, Sep 2002.

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O. Besson and P. Stoica, "Decoupled estimation of DOA and angular spread for a spatially distributed source", IEEE Trans. Signal Processing, vol. 48, no. 7, pp. 1872-1882, Jul 2000.

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A Space-Diffused Spatial-Temporal ARray (STAR) Receiver for DS-CDMA System [13]

P. D. Karaminas and

A. Manikas, "Superresolution Broad Null Beamforming for Co-channel

Interference Cancellation in Mobile Radio Networks", IEEE Transactions on Vehicular Technology, vol. 49, no. 3, pp. 689-697, May 2000. [14]

Jason W.P. Ng and A. Manikas, "Diversely polarised arrays in DS-CDMA: A space-time channel estimation approach", Int. Conf. Acoust., Speech, Sig. Proc., vol. 3, pp. 2617-2620, May 2002.

[15]

Jason W.P. Ng and A. Manikas, "Polarisation-Angle-Delay Estimation using crossed-dipole array for DSCDMA systems", 14th Int. Conf. DSP, vol. 1, pp. 259-262, July 2002.

[16]

A. Manikas and Jason W.P. Ng, "Crossed-Dipole Arrays for Asynchronous DS-CDMA Systems", IEEE Trans. Antennas Propagation, accepted for publication, Sep 2003.

[17]

D. Asztely, B. Ottersten and A.L. Swindlehurst, "Generalised array manifold model for wireless communication channels with local scattering", IEE Proc. Radar, Sonar and Navig., vol. 145, no. 1, pp. 51-57, Feb 1998.

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D. Asztely and B. Ottersten, "The effects of local scattering on direction of arrival estimation with MUSIC", IEEE Trans. Signal Processing, vol. 47, no. 12, pp. 3220-3234, Dec 1999.

[19]

T. S. Naveendra and A. Manikas, "Spatio-temporal Array (STAR) DS-CDMA systems: Localized scattering channel estimation", Global Telecoms Conf., Nov 2002.

[20]

J. C. Liberti and T. S. Rappaport, Smart antennas for wireless communications: IS-95 and third generation CDMA applications, Prentice Hall PTR, Upper Saddle River, Apr 1999.

[21]

D. H. Johnson and D. E. Dudgeon, Array Signal Processing: Concepts and Techniques, PTR Prentice Hall, Englewood Cliffs, Feb 1993.

Page 22

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